%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI699_1 : TPTP v9.0.0. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 05:40:51 PM UTC 2025
% Result : Unsatisfiable 3.34s 1.86s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 103 ( 25 atm; 39 fun; 31 num; 8 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 5 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(y,type,
y: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff(z,type,
z: $int ).
tff(x,type,
x: $int ).
%Foreground operators:
tff(f_58,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_33,axiom,
$product($product(2,z),z) = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f_32,axiom,
$lesseq(0,$sum($product($product(z,z),x),$product($uminus(1),$product(y,x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq3) ).
tff(f_30,axiom,
$greater(x,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq1) ).
tff(f_31,axiom,
$greater(y,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq2) ).
tff(f_83,axiom,
! [A: $int,B: $int] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).
tff(c_53,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_9,plain,
$product($product(2,z),z) = y,
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_37,plain,
$product(2,$product(z,z)) = y,
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_76,plain,
$product(z,z) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_37]) ).
tff(c_63,plain,
$product(z,z) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_37]) ).
tff(c_56,plain,
$product(2,$product(z,z)) = y,
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_70,plain,
y = $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_56]) ).
tff(c_6,plain,
$lesseq(0,$sum($product($product(z,z),x),$uminus($product(y,x)))),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_41,plain,
~ $less($product($product(z,z),x),$product(y,x)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_234,plain,
~ $less($product('#skE_1',x),$product($product(2,'#skE_1'),x)),
inference(demodulation,[status(thm),theory(equality)],[c_53,c_76,c_53,c_70,c_53,c_53,c_41]) ).
tff(c_237,plain,
~ $less(0,$product('#skE_1',x)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_234]) ).
tff(c_239,plain,
$product('#skE_1',x) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_237]) ).
tff(c_238,plain,
~ $less(0,$product('#skE_1',x)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_234]) ).
tff(c_246,plain,
~ $less(0,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_239,c_238]) ).
tff(c_1,plain,
$greater(x,0),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_43,plain,
$less(0,x),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_3,plain,
$greater(y,0),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_42,plain,
$less(0,y),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_71,plain,
$less(0,$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_70,c_42]) ).
tff(c_74,plain,
$less(0,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71]) ).
tff(c_249,plain,
$product('#skE_1',x) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_237]) ).
tff(c_44,plain,
! [A_27: $int,B_28: $int] :
( $less(0,$product(A_27,B_28))
| ~ $less(0,A_27)
| ~ $less(0,B_28) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_298,plain,
( $less(0,'#skE_2')
| ~ $less(0,'#skE_1')
| ~ $less(0,x) ),
inference(superposition,[status(thm),theory(equality)],[c_249,c_44]) ).
tff(c_378,plain,
$less(0,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_43,c_74,c_298]) ).
tff(c_380,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_246,c_378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI699_1 : TPTP v9.0.0. Released v6.3.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 15:17:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.34/1.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.87
% 3.34/1.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------